3. LENSED QUASARS AND H0

In 1964, the Norwegian astronomer Sjur Refsdal proposed an original
method
(Refsdal 1964)
to use gravitational lensing as a tool to
measure the size/age of the Universe. When photons propagate from a
distant source toward the observer, they are under the effect of the
gravity field of lenses along the line of sight. They do not follow a
straight line anymore, but their trajectory is curved and longer than
the original one. As a consequence, it takes more time for the
photons to travel from a lensed source than from an unlensed one. The
geometrical difference introduced by the lens between the two,
lensed and unlensed paths, introduces a time-lag between the arrival
times of the (lensed and unlensed) photons at the position of the
observer. This time lag is called the geometrical "time-delay",
tgeom. While passing in the immediate vicinity of the
gravity field of the lens, the light is affected by a second delay:
the gravitational time-delay, tgrav. A "lensed photon"
will be seen by an observer with a total time-delay
ttot = tgeom +
tgrav, with respect to the observation of the
same photon if it were not lensed.

The time-delay is a function of image position in projection on the
plane of the sky. One can then define an arrival time surface
that associates, to each position on the sky, a given a value of the
time-delay. Most of this surface is missed by the observer who has
only access to the few areas where the lensed images form. When two
or more images of the source are observed it is possible to compare
the arrival times at the positions of the lensed images and to
determine a "relative time-delay". This is in fact the only truly
measurable quantity, rather than the actual time-delay between the
lensed and unlensed paths to the source, since the unlensed source is
never visible.

In practice, time-delays are measured taking advantage of a lensed
source with significant photometric variations. Due to the
time-delay, the variations will be detected by the observer at
different times in the light curves of each image. The shift in time
between the light curves is simply the (total) time-delay between the
images.
Refsdal (1964)
proposed to measure time-delays in lensed
supernovae, but his method was published just when the first quasars
were discovered
(Schmidt 1963).
Quasars, that later turned out to be
very numerous in the sky, rather bright, and photometrically variable,
were promising objects to measure time-delays if at least some of them
were found to be lensed. They appeared in any case much more
promising than rare and transient phenomena such as supernovae.
Indeed, thousands of quasars are now known, and several tens of them
are lensed. Measured quasar time-delays span over a broad range of
values, between days and months. One is larger than a year:
Q 0957+561 (e.g.,
Vanderriest et al. 1989).